Nonparametric estimation of the entropy using a ranked set sample

TL;DR

This paper introduces a new nonparametric entropy estimator based on ranked set sampling, analyzes its theoretical properties, compares it with existing methods, and demonstrates its practical applications through simulations and real data examples.

Contribution

It proposes a novel entropy estimator using ranked set sampling and studies its theoretical properties and practical performance, extending nonparametric entropy estimation methods.

Findings

The estimator performs well in simulations compared to rivals.

It effectively estimates mutual information and Kullback-Leibler divergence.

Applications to real data demonstrate its practical utility.

Abstract

This paper is concerned with non-parametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random sampling. The applications of the proposed estimator to the mutual information estimation as well as estimation of the Kullback-Leibler divergence are provided. Several Monte-Carlo simulation studies are conducted to examine the performance of the estimator. The results are applied to the long-leaf pine (pinus palustris) trees and the body fat percentage data sets to illustrate applicability of theoretical results.